Parametric Synthesis of the Control System of the Balancing Robot by the Numerical Optimization Method

Abstract

This article is devoted to parametric synthesis of a control system of a two-wheeled balancing robot. From the mathematical point of view, the robot is an inverted pendulum type object with a pivot point placed on the wheel axis. This device is unstable while deenergized. Devices of this type are excellent labor atory stands for testing and debugging control algorithms of unstable nonlinear systems. The inverted pendulum math model is well studied theoretically but, when designing a particular device many additional tasks arise such as taking into account the error in measuring the tilt angle and the influence of actuator nonlinearities. In this paper, one of these tasks is solved, namely, the problem of reducing the amplitude of the robot’s oscillation around the equilibrium position. In practice, this oscillation almost always occurs in such systems and leads to various negative effects, such as increased energy consumption, increased wear of an actuator and heating of its windings, etc. Therefore, reducing the amplitude of the oscillation is an important task. To solve this task, the authors of the article propose to use the method of numerical optimization of the regulator, which is well recommended for solving many problems. The article analyzes the behavior of the device near the equilibrium position and identifies the causes of the self-oscillation. Further the method of its simulation is proposed. On the basis of numerical experiments, the main reason for the increase in the amplitude of the oscillation is revealed. The reason is an overlay of the reverse peak of the device transient process on the peak caused by a torque throw. The throw is generated by a combination of actuator backlash and static friction effects which cause the robot self-oscillation. The authors propose a technique of adjusting the regulator, aimed at reducing the magnitude of the reverse peak of the transition process and, as a consequence, reducing the amplitude of the oscillation. The effectiveness of the technique is confirmed experimentally by the results of numerical simulation of the robot’s behavior and the results of testing the coefficients obtained in a real device. The use of the technique allowed reducing the oscillation amplitude in a real device by almost three times.